The basis number of the semi-strong product of special graphs

الملخص EN

The basis number of a graph G is the smallest positive integer k such that the cycle space of G has a k-fold basis.

The semi-strong product of two disjoint graphs G and H is the graph G*H defined by Teh and Yap [13].

In this paper we prove that the basis number of Pn*Pm, Pn*Cm and Cn*Pm is 3, and of Cn*Cm is not more than 4.

Moreover, it is proved that the bais number of Pn*Kmand Cn*Km is 4.